On Gaussian Brunn-Minkowski inequalities

Franck Barthe (1) , Nolwen Huet (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also allows us to have semigroup proofs of the geometric Brascamp-Lieb inequality and of the reverse one which follow exactly the same lines.

Mots clés: Brunn-Minkowski; Gaussian measure; Heat equation; Brascamp-Lieb inequalities

Domaines: Probabilités [math.PR]

Franck Barthe, Nolwen Huet. On Gaussian Brunn-Minkowski inequalities. Studia Mathematica, 2009, 191 (3), pp.283--304. ⟨hal-00270555v2⟩